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oai:docta.ucm.es:20.500.14352/936362025-03-22T00:51:33Zcom_20.500.14352_14col_20.500.14352_15

Capel, Ángela Lucia, Angelo Pérez García, David 2024-01-17T14:05:52Z 2024-01-17T14:05:52Z 2018 Capel Á, Lucia A and Pérez-García D 2018 Quantum conditional relative entropy and quasi-factorization of the relative entropy J. Phys. A: Math. Theor. 51 484001 1751-8121 10.1088/1751-8121/aae4cf https://hdl.handle.net/20.500.14352/93636 https://doi.org/10.1088/1751-8121/aae4cf The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a mixing condition in the Gibbs measure associated to their dynamics, via a quasi-factorization of the entropy in terms of the conditional entropy in some sub-σ-algebras. In this work we analyze analogous quasi-factorization results in the quantum case. For that, we define the quantum conditional relative entropy and prove several quasi-factorization results for it. As an illustration of their potential, we use one of them to obtain a positive log-Sobolev constant for the heat-bath dynamics with product fixed point. eng restricted access Quantum conditional relative entropy and quasi-factorization of the relative entropy journal article